I want to make animations, is Blender the right program for me?
Blender is definitely a good program to use, seeing your purpose. It just needs a bit of patience and practice.

And  about saving actions — it can be done using the action editor in the Blender interface, so that you can use it multiple times. Though you should go through some tutorials on how to do this. There are numerous tutorials on YouTube that explain this functionality. Here's a link.